How can I have a computer learn the equation with known dependent variables?
You might want to try symbolic regression. This is a machine learning approach that tries to generate an equation with arbitrary form that best fits a set of examples. I've used it before when working with physicists who wanted an equation in terms of known numeric constants and specific variables, but didn't expect the equation to be linear or one of the other shapes for which we have standard regression models.

Symbolic regression often (usually?) uses genetic programming for the underlying optimization. A decent tool is Eureka. It used to be free, but I think they want a payment now. You can also do it yourself from any genetic programming toolkit with a little know-how.